How do I freeze the wave modifier animation?
You can freeze the wave by animating the 'Offset' field inversely to the frame advance.

Supposing you have a wave with a positive speed, and at frame 0, it has an Offset of 2. You want to freeze the wave between frame 100 and frame 140.

Then at frame 100, you want an Offset of 2, at frame 101 an Offset of 3, up to frame 140, an Offset of 142. (The offset direction seems topsy-turvy to me, but that's the way it is)

(You could either do this with a driver...)

Or, if there are no interfering variables,  keyframe the Offset value to 2 at frame 100, and 142 at frame 140. 

Then go to the Graph Editor, hit T on the start and end keyframes, and set the interpolation to 'Linear' to get rid of the easing, which would screw the linear relationship you're looking for.